Signal waveforms are used to visualise and explain the equation for the Fourier Transform.
Something I should have been more clear about in the video, is that the equation I wrote is the inverse FT, not the FT. The reason I did this is that I like to start by thinking about the time domain signal x(t) (ie. the actual signal that we observe in the real world), because time is one of the main dimensions that we observe/experience, and we are familiar with signals in this domain. I wrote the equation for the time domain signal in terms of the frequency components (which is actually the Inverse Fourier Transform equation). Once you see the signal from this perspective (ie. as being made up of a sum of individual single-frequency waveforms), then you will understand that there are two ways of viewing the same signal (ie. time-domain and frequency-domain), and that they are related by the Fourier Transform and the Inverse Fourier Transform. That's the important point.
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1 окт 2024